The following are samples of topics that are worthy of semester papers. You may not use these topics for your seminar paper, but you may use the topics as sources of ideas.
International Economics and Fiscal Policy
The purpose of this model is to examine the behavior of the governments of three countries with respect to fiscal policies and economic growth. In this model, we assume that the world is comprised of three countries. Each country can produce either (or both) of two products. Consumers are assumed to have identical preferences across countries. Firms are assumed to be competitive and to have identical production functions across countries. Each country’s government must raise G dollars to fund its operations. That money can be raised via any (or a combination of) three sources: (1) a proportional income tax on consumers, (2) a sales tax on goods purchased by the country’s consumers, or (3) a tariff on foreign goods purchased by the country’s consumers. The model attempts to address the question: What form (or combination of forms) of taxation generate the desired tax revenue while achieving the greatest welfare for the country’s consumers?
Societies maintain cohesion, in part, through a system of morés – behavior that is considered socially acceptable. In developed societies, more important morés are officially encoded into laws. This permits an official social response to those who violate the morés (e.g. fines, imprisonment, death). In less developed societies as well as in societal sub-groups that do not enjoy the force of law, the only punishment for violating morés is exclusion from the society (or sub-group). The purpose of this model is to examine the behavior of individuals who gain utility from violating morés but in so doing, increase the probability of being banished from society. The probability of being banished is a negative function of the compatibility of an individual’s behavior with the morés of those around him. The model attempts to address the following questions: (1) What is the impact on the individual of the society being proximate to an antagonistic enemy (to which the banished member would be vulnerable)? (2) What is the impact on the likelihood of anti-social behavior as the society’s governance moves along a continuum from anarchy to totalitarianism? (3) What is the likelihood of sub-groups with different morés evolving within the same society and what does the model predict about the optimal size of sub-groups relative to the population as a whole?
A consumer is faced with choosing a single brand from among many brands with different attributes. The consumer is not aware of all of the brands that exist and is aware of his lack of information. The consumer derives utility from consuming a brand that is most compatible with his tastes and derives disutility from collecting information about brands and their attributes. At the time of selection, the consumer assesses a brand’s attributes with error. Only after consuming the brand is the consumer fully aware of the brand’s attributes. This model attempts to answer the questions: (1) For a given brand, X, what impact does an increase in the number of brands similar to X have on the consumer’s demand for X? (2) For a given brand, X, what impact does an increase in the uncertainty about other brands’ attributes have on the consumer’s demand for X.
August 13, 2009 6:59 PM PDT
How to use math to choose a wife
by Chris Matyszczyk
Perhaps the subject most fascinating to me at the moment is the gamble that is involved in choosing a life partner.
Perhaps I have been unnecessarily haunted since research revealed that Facebook destroys romantic relationships. Still, it was quite odd that a man whom I have chosen to follow on Twitter for his remarkable erudition in social psychology (oh, alright, his name is Dominic Johnson) passed along a quite extraordinary article from New Scientist, one that has made me ponder more deeply than I usually care to.
While the article begins by discussing the mathematical ways in which you can improve your chances in Vegas (or, if your taste and eyes have deserted you, Atlantic City), it goes on to discuss the marriage problem. Apparently, mathematicians have tortured themselves over marriage for some years. I did not know this. I figured that perhaps mathematicians only ever had one girlfriend, whom they married very soon after sex.
May I go down on one knee and admit how wrong I was?
Mathematicians have racked their brains and abacuses, for the good of society, in order to help us all choose wisely the person who shares our king-size. According to New Scientist, the law of diminishing returns has long been thought to be a marvelous indicator of when to stick, rather than turn another card.
Naturally, scientific laws have certain suppositions. And at first glance, I considered the idea of having a mere 100 choices a little unrealistic.
Were they each the other's 38th choice?
(Credit: CC Simon Shaw/Flickr)
However, the more I thought about it, the more it seemed a little more natural than it might have appeared. We march our way merrily through life, meeting people and declaring them a "yay" or a "nay."
Oh, we have some supposed criteria in our heads about what makes a "yay"- body type, nose shape, or some such nonsense. But commitment is a very hairy creature, one that barks at us more often than it sings.
So for a long time, mathematicians believed that, given 100 choices (each of which has to be chosen or discarded after the interview) you should discard the first 50 and then choose the next best one. (The assumption also is that if you don't choose the first 99, you have to choose number 100, which, again, seems rather realistic to me. I know so many people who have chosen the last resort out of perceived necessity rather than, say, happiness.)
The "Discard 50 then Choose the Next Best" method apparently gives you a 25 percent chance of choosing the best candidate.
However, then along came John Gilbert and Frederick Mosteller of Harvard University. I do not believe they were married. However, they came upon the idea that the magic number is, in fact, 37. Yes, you should stop after 37 candidates and choose the next best one. This number was apparently derived by taking the number 100 and dividing by e, the base of the natural logarithms (around 2.72). And it apparently increases your chances of the best choice to 37 percent.
Here's the real beauty of this calculation, though. You don't have to limit yourself to 100. This optimization works for any population. So if you have a world of 26 potential life partners, simply divide by 2.72 and choose the next best one.
Now, I know it is sometimes hard to know exactly how many potential partners are in your firmament. But it is surely not beyond some calculation.
We need a little more stability in this world. We need more happiness. And we need just a little more good judgment. It seems that only math can save us.
There is a small word of warning, however. Some psychologists, such as JoNell Strough at West Virginia University, believe that the more we invest (in a gambling and, one supposes, marriage context), the more likely our decision will be attached to disaster.
However, I would be interested whether any of you number-conscious geniuses out there have also used mathematical principles to choose your betrothed. Perhaps you have done it more than once, but we would still love to hear your number-based criteria.
November 2, 2005